Place the potatoes in a medium pot and cover with cold salted water. Bring to a boil, lower the heat and simmer until tender when pierced with a knife. Drain the potatoes and return to the pot over low heat. Stir the potatoes for a couple of minutes to dry them out. Add the milk, butter, cheese, and green onions, then mash with a hand masher until smooth. Season with sea salt and white pepper, to taste.
Heat the olive oil in a large nonstick skillet over medium heat. Add the carrots and onions; cook until tender and beginning to brown, about 5 minutes. Add the turkey and thyme, and continue to cook, breaking the turkey up with a spoon, until the turkey is cooked through and lightly browned. Add the minced garlic, and cook, for 30 seconds then add the ketchup and Worcestershire sauce then cook until lightly caramelized. Stir the chicken broth and flour together in a small bowl until smooth, and then pour into the skillet. Cook until thickened, about 2 minutes. Season with sea salt and freshly cracked pepper, to taste.
Coat the baking dishes with cooking spray. Ladle the turkey mixture evenly into the baking dishes. Spoon the mashed potatoes over the filling.
Place into the oven and bake until the potatoes are lightly browned and the turkey filling is bubbly around the edges, 10 to 15 minutes. Sprinkle with Green Onions. Let the cottage pies cool for 5 minutes before serving. Enjoy.